Specker sequence

Okay kiddo, have you ever tried putting puzzle pieces together? Sometimes it gets a bit tricky when you don't know which piece goes where, right? Now, imagine you have a super special puzzle that needs to be put together in a specific order, or sequence.

The Specker sequence is sort of like the instructions for putting that puzzle together. It's a special way of putting numbers in order where each number is different from the ones before it by a certain amount.

Let's say we start with the number 1. The next number in the sequence would be 4 (because we added 3 to 1). The number after that is 7 (because we added 3 again). And we keep going like that, adding 3 every time, until we get to the number 16.

So the Specker sequence would look like this: 1, 4, 7, 10, 13, 16.

It might seem a little random, but there's actually a really cool pattern to it! If you look closely, you'll notice that there are no repeats in the sequence. And every number between 1 and 16 is included in the sequence exactly once.

Isn't that neat? So, in short, the Specker sequence is a special way of putting numbers in order, where each number is different from the ones before it by a certain amount. It's like a special list, but with no repeats!